Uniqueness of characterization of absolutely continuous distributions by regressions of generalized order statistics |
| |
Authors: | Mariusz Bieniek Krystyna Macia̧g |
| |
Affiliation: | 1.Institute of Mathematics,Maria Curie Sk?odowska University,Lublin,Poland;2.Ernst and Young Ltd.,Warsaw,Poland |
| |
Abstract: | We provide a new approach to the problem of the unique identification of distributions with a continuous density by a single regression function of order statistics or record values or, more generally, generalized order statistics. Using their Markov property we show that the characterization is unique if and only if the corresponding system of differential equations has the unique solution. This result is new even in the particular case of ordinary order statistics. This approach provides a new proof of characterization of power, exponential and Pareto distributions by linearity of corresponding regression. It also yields new examples of characterizations of distributions. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|